Question

How do you easily and quickly find the equation of a line and a plane in r 3?

Answer 1

I think something's missing from your problem statement. Do you mean "intersection"?

Answer 2

no i mean seperately
a line
and then a plane.

Answer 3

in calculus

Answer 4

There are several different forms of the equation of a line in 3D space.
Similarly, there are several forms of the equation of a plane in space.

How do you most often learn your material? Do you have a suitable textbook?

Answer 5

im taking an online calculus course.

Answer 6

Hope you have a consistent and effective way of summarizing the concepts and formulas involved. Do you have some kind of online reference book? Access to an e-book? I can help with questions such as yours, but would prefer you'd already done some research and reading before I step in.

Answer 7

I've watched the videos from the course but I don't understand how to get the equation. I understand that a line has 3 equations, one for x, one for y, and one for z.

Answer 8

I am reluctant to just give y ou the equations you want, since a lot depends upon your ability to research such info online and to copy it down for later study and review.

Do you want the equations themselves or do you want to undrstand how to derive them?

I've worked with this material quite a bit, but it's been some months, and I'd thus need to look up some of this info in a textbook I have on hand.

Please state your goal. What, specifically, would you like to get from me?

Answer 9

I want to be able to know how to derive them and how to use them.

Answer 10

That's an admirable goal.
To help you with the derivation, I'd definitely need to fetch my textbook and review it myself.

Here's a starter: supposing that (a, b,c) is a point in space, and that we want the equation of a line in the direction v=<c,d,e>.

The equation of that line, as a vector quantity, is \[r=r _{0}+tv\]
where r-sub-0 is the vector from the origin to the point (a,b,c) in space and v is the direction vector. Does this look at all familiar? t is a parameter.

Answer 11

Example: Supposing that we want to find the equation of the line through the point P(1, 2,-1) with direction v=<1,1,1>.

then the vector equation of the line is r=<1,2,-1>+t<1,1,1>.

Answer 12

How are you doing in this course in general? Without having worked with you before, I have no idea of where you're coming from in understanding this material or what kind of help you most need at the moment.

Answer 13

I'm very happy to help, David, but I cannot and do not want to be your primary source of info. Rather, I'll guide you, answer questions, make suggestions on how to learn the material, and so on.

Answer 14

@DavidUsa ?

Answer 15

hi im reading what u wrote

Answer 16

the specific chapter that this stuff is in is the "vector calculus chapter." i understand vectors, the i j k vectors, dot products, and cross products, but im stuck on finding the equation of a plane and a line.

Answer 17

can you show me an example of how to do it? it would be really helpful

Answer 18

Example: Supposing that we want to find the equation of the line through the point P(1, 2,-1) with direction v=<1,1,1>.

then the vector equation of the line is r=<1,2,-1>+t<1,1,1>.

Answer 19

If I give you and example and it's not clear to you, help me help you by asking questions.

Answer 20

ok

Answer 21

Awaiting your next response.

Answer 22

ok next

Answer 23

i understand

Answer 24

do you have a textbook, or are you dependent upon online learning materials for this course?

Answer 25

I'll let you lead this discussion. Where to next?

Do you have a textbook, or are you dependent upon online learning materials for this course?

Answer 26

i dont have a textbook.

Answer 27

We need to work out a plan, then, for you to obtain, learn and practice the course content. Is it possible (or legal) for you to share your online reference materials, so that I'd know what you have (or don't have)?

Answer 28

Example: Supposing that we want to find the equation of the line through the point P(1, 2,-1) with direction v=<1,1,1>.
then the vector equation of the line is r=<1,2,-1>+t<1,1,1>.
hmm...

Answer 29

Since I'm deaf, I can't imagine trying to learn this stuff without a textbook.
If you can't share your online materials, could you at least describe what they tell you about the equations of lines in space? I have an appropriate textbook here.

Answer 30

i got it! i can send u the notes from that video. its in pdf form

Answer 31

Great! Send me the notes just for equations of lines in space, for now.

Answer 32

wrgnsc@rit.edu
or use Attach File

Answer 33

there

Answer 34

Wonderful! So clear!
Now, it's your job to tell me what you'd like for me to do to help you understand this material. I can't promise I'll do everything you want, but will do whatever I think is reasonable.

Answer 35

This is what we were just doing (in that example problem):

Given a point on a line, and a vector parallel to the line, find the vector equation of the line,

Answer 36

ok.

Answer 37

David? You were typing something for quite a while.

Answer 38

it says im writing even when im not sometimes. also i had to refresh the page because my computer was lagging

Answer 39

David, please let me know your status. Want to continue this discussion? Now or later? Unsure of your intent.

Answer 40

do u want to watch the video?

Answer 41

lets do it now

Answer 42

im lagging sorry

Answer 43

do u have a gmail?

Answer 44

i know how u can watch the video without me giving the password

Answer 45

No, thanks. I'd prefer that you watch it and then phrase questions about whatever content of that video is not clear to you. The clearer you can be in your questions, the better. Since I'm deaf, I'd miss the audio part of the video anyway. The pdf document you've shared is great and is all I need.

Answer 46

does it have audio? If so, i would not hear (or understand) the audio part.

Answer 47

ok

Answer 48

i got it

Answer 49

OK. The ball's in your court. What would you like to discuss?

Answer 50

well theres a little board on the side of the video that has the stuff that hes saying.

Answer 51

not his words but the content

Answer 52

go to ur email please